Matrix expression of finite Boolean-type algebras

NILPOTENT GRAPHS OF MATRIX ALGEBRAS

Let $R$ be a ring with unity. The undirected nilpotent graph of $R$, denoted by $Gamma_N(R)$, is a graph with vertex set ~$Z_N(R)^* = {0neq x in R | xy in N(R) for some y in R^*}$, and two distinct vertices $x$ and $y$ are adjacent if and only if $xy in N(R)$, or equivalently, $yx in N(R)$, where $N(R)$ denoted the nilpotent elements of $R$. Recently, it has been proved that if $R$ is a left A...

Hypercontractivity in Finite-dimensional Matrix Algebras

We obtain hypercontrativity estimates for a large class of semigroups defined on finite-dimensional matrix algebras Mn. These semigroups arise from Poisson-like length functions ψ on Zn × Zn and provide new hypercontractive families of quantum channels when ψ is conditionally negative. We also study the optimality of our estimates.

On possibility and probability measures in finite Boolean algebras

Robbins Algebras vs. Boolean Algebras

In the early 1930s, Huntington proposed several axiom systems for Boolean algebras. Robbins slightly changed one of them and asked if the resulted system is still a basis for variety of Boolean algebras. The solution (afirmative answer) was given in 1996 by McCune with the help of automated theorem prover EQP/OTTER. Some simplified and restucturized versions of this proof are known. In our vers...

Cluster-tilted Algebras of Finite Representation Type

We investigate the cluster-tilted algebras of finite representation type over an algebraically closed field. We give an explicit description of the relations for the quivers for finite representation type. As a consequence we show that a (basic) cluster-tilted algebra of finite type is uniquely determined by its quiver. Also some necessary conditions on the shapes of quivers of cluster-tilted a...